Review of Elastic Analysis of Box Girder Bridges

The importance of thin-walled box girder bridges has attracted the attention of researchers since the last five decades. A lot of literature has dealt with the analytical formulations as well as experimental investigations. Field studies have increased tremendously in the last decade. So far the agreement between the analytical and experimental results has been excellent and, therefore, has made it possible to augment a limited number of experimental tests with hundreds of analytical studies. Highlights of research efforts in published literature regarding the analysis methods and experimental studies related to the elastic analysis of box girder bridges have been presented in this review. Subjects discussed include: (1) Thin –Walled Curved Beam Theory; (2) BEF/EBEF Method; (3) Finite Segment Method; (4) Folded Plate Method; (5) Finite Difference Method; (6) Energy Variational Principle; (7) Grillage Analogy and Space Frame Methods; (8) Finite Element Method; (9) Finite Strip Method; (10) Simplified/Miscellaneous Methods; (11) Experimental  Studies.http://dx.doi.org/10.4314/njt.v34i1.1

Recent developments on refined theories for beams with applications

This paper is a review of the most influential approaches to developing beam models that have been proposed over the last few decades. Essentially, primary attention has been paid to isotropic structures while a few extensions to composites have been given for the sake of completeness. Classical models - Da Vinci, Euler-Bernoulli, and Timoshenko - are described first. All those approaches that are aimed at the improvement of classical theories are then presented by considering the following main techniques: shear correction factors, warping functions, Saint-Venant based solutions and decomposition methods, variational asymptotic methods, the Generalized Beam Theory and the Carrera Unified Formulation (CUF). Special attention has been paid to the latter by carrying out a detailed review of the applications of 1D CUF and by giving numerical examples of static, dynamic and aeroelastic problems. Deep and thin-walled structures have been considered for aerospace, mechanical and civil engineering applications. Furthermore, a brief overview of two recently introduced methods, namely the mixed axiomatic/asymptotic approach and the component-wise approach, has been provided together with numerical assessments. The review presented in this paper shows that the development of advanced beam models is still extremely appealing, due to the computational efficiency of beams compared to 2D and 3D structural models. Although most of the techniques that have recently been developed are focused on a given number of applications, 1D CUF offers the breakthrough advantage of being able to deal with a vast variety of structural problems with no need for ad hoc formulations, including problems that can notoriously be dealt with exclusively by means of 2D or 3D models, such as complete aircraft wings, civil engineering constructions, as well as multiscale and wave propagation analyses. Moreover, 1D CUF leads to a complete 3D geometrical and material modeling with no need of artificial reference axes/surfaces, reduced constitutive equations or homogenization techniques

Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures

This paper presents three beam Finite Element (FE) formulations developed for the analysis of thin-walled structures. These account for out-of-plane cross-section warping by removing the classical rigid body cross-section hypothesis and capture the interaction of axial/bending stress components with shear and torsion. The beam FE models rely on different kinematic assumptions to describe out-of-plane cross-section deformations. Indeed, warping displacement field is interpolated in the element volume according to different approaches, with increasing level of accuracy and detail. First two models adopt a coarse warping description, where warping displacement field is defined as the linear combination of assumed warping profiles and unknown kinematic parameters. In the first model, these are considered as equal to the generalized cross-section torsional curvature and shear strains and a classical displacement-based formulation is adopted to derive the element governing equations. In the second model, warping parameters are assumed as independent kinematic quantities and a mixed approach is considered to derive the FE formulation. Third model, also relying on a mixed formulation, independently interpolates warping by introducing additional degrees of freedom on the cross-section plane, thus, resulting in a richer description of the out-of-plane deformations. This latter is also adopted to propose a numerical procedure for the warping profile evaluation of thin-walled beams subjected to torsional and shear forces, for general cross-section geometry. The efficiency and accuracy of the proposed FE formulations are validated by simulating the response of thin-walled structures under torsion and coupled torsion/shear actions and the influence of the kinematic assumptions characterizing each formulation is discussed

A general finite element system with special reference to the analysis of cellular structures

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Design analysis of single-span advanced composite deck-and-stringer bridge systems

The advantages of advanced composite materials (ACM) over conventional materials motivate their use in highway bridges for rehabilitation and replacement of structures. However, the complexity of the composites has created a need for simplified design analysis procedures that account for both the geometry and material properties of ACM members and systems.;An analytical/experimental study of fiber-reinforced plastic (FRP) composite bridges consisting of cellular box decks and wide-flange I-beams as stringers is presented. The design analysis covers: (1) ply stiffnesses and strengths; (2) laminate engineering stiffnesses; (3) apparent stiffness properties for composite decks; and (4) stringer stiffness properties. Finite element modeling is used to verify the accuracy of the design analysis.;For design analysis of FRP deck-and-stringer bridge system, an approximate series solution for orthotropic plates including first-order shear deformation is developed. Based on the analytical/experimental study, simplified design equations are developed for bridge applications, which include global design of deck-and-stringer system accounting for load distribution factors

Curved Steel Bridge Research Project, Interim Report I: Synthesis

DTFH61-93-C-00136The objectives of the FHWA Curved Steel Bridge Program are (1) to conduct fundamental research into the structural behavior of curved steel flexural members and bridges, and (2) to address construction issues, in order to provide adequate information to develop and clarify design specifications. The work under this program is a coordinated effort between the Transportation Research Board (TRB), the Federal Highway Administration (FHWA), and participating States under a Highway Planning and Research (HP&R) Pooled Fund Study. This program focuses on four areas: (1) synthesis of work that has been done since the Consortium of University Research Teams (CURT) Project; (2) update of the current specification in a load factor design format; (3) conduct of research recommended by Structural Stability Research Council's (SSRC's) Task Group 14 at the April 14-15, 1991 workshop; and (4) development of a load and resistance factor design specification based on research conducted area 3. Areas 1 and 3 are conducted by FHWA as a pooled fund study with an administrative contract. Area 2 is conducted by TRB under the National Cooperative Highway Research Program (NCHRP) Project 12-38. Area 4 is proposed to be addressed by NCHRP at a future date. This report summarizes the results of a comprehensive literature search under the FHWA research program

Strong-form governing equations and solutions for variable kinematic beam theories with practical applications

Due to the work of pioneering scientists of the past centuries, the three-dimensional theory of elasticity is now a well-established, mature science. Nevertheless, analytical solutions for three-dimensional elastic bodies are generally available only for a few particular cases which represent rather coarse simplifications of reality. Against this background, the recent development of advanced techniques and progresses in theories of structures and symbolic computation have made it possible to obtain exact and quasi-exact resolution of the strongform governing equations of beam, plate and shell structures. In this thesis, attention is primarily focused on strong-form solutions of refined beam theories. In particular, higher-order beam models are developed within the framework of the Carrera Unified Formulation (CUF), according to which the three-dimensional displacement field can be expressed as an arbitrary expansion of the generalized displacements. The governing differential equations for static, free vibration and linearized buckling analysis of beams and beam-columns made of both isotropic and anisotropic materials are obtained by applying the principle of virtual work. Subsequently, by imposing appropriate boundary conditions, closed-form analytical solutions are provided wherever possible in the case of structures with uncoupled axial and in-plane displacements. The solutions are also provided for a wider range of structures by employing collocation schemes that make use of radial basis functions. Such method may be seriously affected by numerical errors, thus, a robust and efficient method is also proposed in this thesis by formulating a frequency dependant dynamic stiffness matrix and using the Wittrick-Williams algorithm as solution technique. The theories developed in this thesis are validated by using some selected results from the literature. The analyses suggest that CUF furnishes a reliable method to implement refined theories capable of providing almost three-dimensional elasticity solution and that the dynamic stiffness method is extremely powerful and versatile when applied in conjunction with CUF

Design of an Origami Patterned Pre-Folded Thin Walled Tubular Structure for Crashworthiness

Indiana University-Purdue University Indianapolis (IUPUI)Thin walled tubular structures are widely used in the automotive industry because of its weight to energy absorption advantage. A lot of research has been done in different cross sectional shapes and different tapered designs, with design for manufacturability in mind, to achieve high specific energy absorption. In this study a novel type of tubular structure is proposed, in which predesigned origami initiators are introduced into conventional square tubes. The crease pattern is designed to achieve extensional collapse mode which results in decreasing the initial buckling forces and at the same time acts as a fold initiator, helping to achieve a extensional collapse mode. The influence of various design parameters of the origami pattern on the mechanical properties (crushing force and deceleration) are extensively investigated using finite element modelling. Thus, showing a predictable and stable collapse behavior. This pattern can be stamped out of a thin sheet of material. The results showed that a properly designed origami pattern can consistently trigger a extensional collapse mode which can significantly lower the peak values of crushing forces and deceleration without compromising on the mean values. Also, a comparison has been made with the behavior of proposed origami pattern for extensional mode verses origami pattern with diamond fold